K-string tensions at finite temperature and integrable models

TL;DR

This paper demonstrates that in a three-dimensional Z_4 gauge model, the ratios of k-string tensions remain constant throughout the entire confining phase, supported by numerical and exact integrable model results.

Contribution

It shows that k-string tension ratios are constant in the whole confining phase of a 3D Z_4 gauge model, extending previous low-temperature findings.

Findings

Ratios of k-string tensions are constant throughout the confining phase.

Numerical experiments support the constancy of tension ratios.

Exact results from an integrable spin model underpin the findings.

Abstract

It has recently been pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.